LEADER 05427nam 2200649Ia 450 001 9910144684203321 005 20170814180908.0 010 $a1-282-30775-4 010 $a9786612307751 010 $a0-470-31702-7 010 $a0-470-31786-8 035 $a(CKB)1000000000687572 035 $a(EBL)469989 035 $a(OCoLC)476291655 035 $a(SSID)ssj0000343236 035 $a(PQKBManifestationID)11264961 035 $a(PQKBTitleCode)TC0000343236 035 $a(PQKBWorkID)10288447 035 $a(PQKB)11428037 035 $a(MiAaPQ)EBC469989 035 $a(PPN)159316480 035 $a(EXLCZ)991000000000687572 100 $a19981030d1999 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aStatistical modeling by wavelets$b[electronic resource] /$fBrani Vidakovic 210 $aNew York $cWiley$d1999 215 $a1 online resource (410 p.) 225 1 $aWiley series in probability and mathematical statistics. Applied probability and statistics section 300 $a"A Wiley-Interscience publication." 311 $a0-471-29365-2 320 $aIncludes bibliographical references (p. 345-370) and indexes. 327 $aStatistical Modeling by Wavelets; Contents; Preface; Acknowledgments; 1. Introduction; 1.1. Wavelet Evolution; 1.2. Wavelet Revolution; 1.3. Wavelets and Statistics; 1.4. An Appetizer: California Earthquakes; 2. Prerequisites; 2.1. General; 2.2. Hilben Spaces; 2.2.1. Projection Theorem; 2.2.2. 0rthonomal Sets; 2.2.3. Reproducing Kernel Hilberf Spaces; 2.3. Fourier Transformation; 2.3.1. Basic Properties; 2.3.2. Poisson Summation Formula and Sampling Theorem; 2.3.3. Fourier Series; 2.3.4. Discrete Fourier Transform; 2.4. Heisenberg's Uncertainty Principle; 2.5. Some Important Function Spaces 327 $a2.6. Fundanzentals of Signal Processing2.7. Exercises; 3. Wavelets; 3.1. Continuous Wavelet Transformation; 3.1.1. Basic Properties; 3.1.2. Wavelets for Continuous Transfonnations; 3.2. Discretization of the Continuous Wavelet Transform; 3.3. Multiresolution Analysis; 3.3.1. Derivation of a Wavelet Function; 3.4. Same Important Wavelet Bases; 3.4.1. Haar's Wavelets; 3.4.2. Shannon's Wavelets; 3.4.3. Meyer's Wavelets; 3.4.4. Franklin s Wavelets; 3.4.5. Daubechies ' Conzpactly Supporled Wavelets; 3.5. Some Extensions; 3.5.1. Regularity of Wavelets 327 $a3.5.2. The Least Asytnmetric Daubechies ' Wavelets: Symrnlets3.5.3. Approxintations and Characterizations of Functional Spaces; 3.5.4. Daubechies-Lagarias Algorithm; 3.5.5. Moment Conditions; 3.5.6. Interpolating (Cardinal) Wavelets; 3.5.7. Pollen-Type Parameterization of Wavelets; 3.6. Exercises; 4. Discrete Wavelet Transformations; 4.1. Introduction; 4.2. The Cascade Algorithnt; 4.3. The Operator Notation of DWT; 4.3.1. Discrete Wavelet Transfomiations as Linear Transfonnations; 4.4. Exercises; 5. Some Generalizations; 5.1. Coiflets; 5.1.1. Construction of Coifrets 327 $a5.2. Biorthogonal Wavelets5.2.1. Construction of Biorthogonal Wavelets; 5.2.2. B-Spline Wavelets; 5.3. Wavelet Packets; 5.3.1. Basic Properties of Wavelet Packets; 5.3.2. Wavelet Packet Tables; 5.4. Best Basis Selection; 5.4.1. Some Cost Measures and the Best Basis Algorithm; 5.5. ?-Decimated and Stationary Wavelet Transformations; 5.5.1. ?-Decimated Wavelet Transformation; 5.5.2. Stationary (Non-Decimated) Wavelet Transformation; 5.6. Periodic Wavelet Transformations; 5.7. Multivariate Wavelet Transfornations; 5.8. Discussion; 5.9. Exercises; 6. Wavelet Shrinkage; 6.1. Shrinkage Method 327 $a6.2. Lineur Wavelet Regression Estimators6.2.1. Wavelet Kernels; 6.2.2. Local Constant Fit Estimators; 6.3. The Simplest Non-Linear Wavelet Shrinkage: Tliresholding; 6.3.1. Variable Selection and Thresholding; 6.3.2. Oracular Risk for Thresholding Rules; 6.3.3. Why the Wavelet Shrinkage Works; 6.3.4. Almost Sure Convergence of Wavelet Sh rinkuge Est imaf ors; 6.4. General Minimax Paradigm; 6.4.1. Translation of Minimaxity Results to the Wavelet Domain; 6.5. Thresholding Policies and Thresholdkg Rides; 6.5.1. Exact Risk Analysis of Thresholding Rules; 6.5.2. Large Sample Properties 327 $a6.5.3. Some Orher Shrinkage Rules 330 $aA comprehensive, step-by-step introduction to wavelets in statistics.What are wavelets? What makes them increasingly indispensable in statistical nonparametrics? Why are they suitable for ""time-scale"" applications? How are they used to solve such problems as denoising, regression, or density estimation? Where can one find up-to-date information on these newly ""discovered"" mathematical objects? These are some of the questions Brani Vidakovic answers in Statistical Modeling by Wavelets. Providing a much-needed introduction to the latest tools afforded statisticians by wavelet theory, 410 0$aWiley series in probability and mathematical statistics.$pApplied probability and statistics. 606 $aMathematical statistics 606 $aWavelets (Mathematics) 615 0$aMathematical statistics. 615 0$aWavelets (Mathematics) 676 $a515.2433 676 $a519.5 700 $aVidakovic$b Brani$f1955-$0288619 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910144684203321 996 $aStatistical modeling by wavelets$9866473 997 $aUNINA